Angle of Elevation and Energy lost to Friction 2010
Tom, Bill
Introduction
Our experiment examines the relationship between the angle of elevation of a ramp and the energy loss due to friction. The experiment is a continuation of the angle of elevation and spring energy experiment. We designed our experiment so that we would be able to test their results, and we tried to improve upon their method. To understand our experiment it is impotent to understand the concept of energy. Energy is a scalar measure of an objects ability to do work. The two types of energy in our experiment are gravitational potential energy, and kinetic energy. The topic of our experiment can be seen throughout history, and many people have experimented with it to find the best way to use ramps. A good example is the Egyptians who many think used ramps to help build the pyramids. In this case friction would matter a lot, because of the weight of the stone blocks. The purpose of our experiment is to retest the results of the angle of elevation and spring energy experiment, and to look for the relation between angle of elevation and energy loss due to friction.
Procedure
For our experiment we used a cart, a track, logger pro, photogate, an inclinometer, a card, and a ruler. We calculated the starting energy of the cart by calculating the Kinetic Energy of the cart the moment it was propelled forward. We calculated the KE by launching a cart with a card taped to the top through a photogate so that the card passed through the photogate on a flat track five times. Using the width of the card and the time it took to pass through the photogate we found the velocity of the cart by using distance over time. After finding the five velocities we massed the cart using a triple beam balance. Using the mass, velocities, and the formula KE=.5mv^2 we found the five KE values. We then took the five KE values and averaged them. We took the inclinometer and used it to place the track at a ten degree angle; after putting the track at a ten degree angle we stacked books up until it held the track up at that angle. We placed the cart on the bottom of the track and measured the length of the cart on the track. We launched the cart up the track five times recording the distance it traveled up the track each time. Using the distance the cart traveled each time minus the length of the cart as the hypotenuse of a right triangle we found the height of the cart above the table by taking the sin of ten degrees multiplied by the hypotenuse. Using the five heights and the formula PE=mgh we calculated the potential energy. Using the five PE values we found the average and found the difference between the starting KE and the PE to find the energy loss due to friction. We repeated this steps for the angles fifteen and twenty.
Results
angle
average PE
10
.2164
15
.2326
20
.2558
angle
energy lost
10
-.003
15
-.0192
20
-.0424
angle
10
15
20
PE
.211
.233
.260
PE
.211
.237
.255
PE
.228
.233
.256
PE
.224
.227
.243
PE
.208
.233
.265
Taking the five original values of PE for ten degrees and performing a 2sampT-test with them and the five values of KE we get a p value of .2326. If we do two more tests for fifteen degrees and twenty degrees we get the p values .0010 and 8.653.
Conclusions
After analyzing the data we found that as the angle increased the energy loss not only decreased, but the cart had more energy. This is impossible, and so we conclude that our experiment's results are untrue. The sources of error in our experiment is that the cart has such low amounts of friction that over the course of the track the amount of energy loss due to friction is an incredibly small amount. The small amount of energy loss magnified the impact of human error caused by marking how high the cart traveled by guessing. To improve our experiment and to reduce the sources of error we could increase the friction of the cart, which would increase the difference in energy allowing the loss of energy to be more easily measured.
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References
Lehrman, Robert L. Barron's E-Z Physics. Hauppauge, NY: Barron's Educational Series, 2009. Print.
"Friction -." Wikipedia, the free encyclopedia. Web. 28 Jan. 2010. <http://en.wikipedia.org/wiki/Friction>.
Table of Contents
Angle of Elevation and Energy lost to Friction 2010
Tom, Bill
Introduction
Our experiment examines the relationship between the angle of elevation of a ramp and the energy loss due to friction. The experiment is a continuation of the angle of elevation and spring energy experiment. We designed our experiment so that we would be able to test their results, and we tried to improve upon their method. To understand our experiment it is impotent to understand the concept of energy. Energy is a scalar measure of an objects ability to do work. The two types of energy in our experiment are gravitational potential energy, and kinetic energy. The topic of our experiment can be seen throughout history, and many people have experimented with it to find the best way to use ramps. A good example is the Egyptians who many think used ramps to help build the pyramids. In this case friction would matter a lot, because of the weight of the stone blocks. The purpose of our experiment is to retest the results of the angle of elevation and spring energy experiment, and to look for the relation between angle of elevation and energy loss due to friction.Procedure
For our experiment we used a cart, a track, logger pro, photogate, an inclinometer, a card, and a ruler. We calculated the starting energy of the cart by calculating the Kinetic Energy of the cart the moment it was propelled forward. We calculated the KE by launching a cart with a card taped to the top through a photogate so that the card passed through the photogate on a flat track five times. Using the width of the card and the time it took to pass through the photogate we found the velocity of the cart by using distance over time. After finding the five velocities we massed the cart using a triple beam balance. Using the mass, velocities, and the formula KE=.5mv^2 we found the five KE values. We then took the five KE values and averaged them. We took the inclinometer and used it to place the track at a ten degree angle; after putting the track at a ten degree angle we stacked books up until it held the track up at that angle. We placed the cart on the bottom of the track and measured the length of the cart on the track. We launched the cart up the track five times recording the distance it traveled up the track each time. Using the distance the cart traveled each time minus the length of the cart as the hypotenuse of a right triangle we found the height of the cart above the table by taking the sin of ten degrees multiplied by the hypotenuse. Using the five heights and the formula PE=mgh we calculated the potential energy. Using the five PE values we found the average and found the difference between the starting KE and the PE to find the energy loss due to friction. We repeated this steps for the angles fifteen and twenty.Results
Taking the five original values of PE for ten degrees and performing a 2sampT-test with them and the five values of KE we get a p value of .2326. If we do two more tests for fifteen degrees and twenty degrees we get the p values .0010 and 8.653.
Conclusions
After analyzing the data we found that as the angle increased the energy loss not only decreased, but the cart had more energy. This is impossible, and so we conclude that our experiment's results are untrue. The sources of error in our experiment is that the cart has such low amounts of friction that over the course of the track the amount of energy loss due to friction is an incredibly small amount. The small amount of energy loss magnified the impact of human error caused by marking how high the cart traveled by guessing. To improve our experiment and to reduce the sources of error we could increase the friction of the cart, which would increase the difference in energy allowing the loss of energy to be more easily measured.==----
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References
Lehrman, Robert L. Barron's E-Z Physics. Hauppauge, NY: Barron's Educational Series, 2009. Print."Friction -." Wikipedia, the free encyclopedia. Web. 28 Jan. 2010. <http://en.wikipedia.org/wiki/Friction>.